Answer
$-\sqrt{15}$, $\sqrt{15}$
Work Step by Step
Given \begin{equation}
2 a^2+6 a-10=6 a+20.
\end{equation}
Rearrange the equation before applying the quadratic formula and determine the contsnats $a$, $b$, $c$: \begin{equation}
\begin{aligned}
2 a^2+6 a-10&=6 a+20\\
2 a^2+6 a-6a-10-20&=0\\
2 a^2-30&=0\\
a =2, b= 0, c&= -30.
\end{aligned}
\end{equation} The quadratic formula gives: \begin{equation}
\begin{aligned}
x&=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\
a &=\frac{0 \pm \sqrt{0^2-4 \cdot 2 \cdot (-30)}}{2 \cdot 2}\\
&=\frac{0 \pm \sqrt{240} }{4}\\
&=\frac{0 \pm \sqrt{16\cdot 15} }{4}\\
&=\frac{0 \pm 4 \sqrt{ 15} }{4}\\
&=\pm \sqrt{15}.
\end{aligned}
\end{equation} The solution is \begin{equation}
a=-\sqrt{15} ,\quad a=\sqrt{15}.
\end{equation}
